Mathematics, 18.10.2019 07:30 dnarioproctor
Find the exact value of csc theta if cot theta = -2 and the terminal side of theta lies in quadrant ii (2).
Answers: 3
![\bf cot(\theta )=\cfrac{\stackrel{adjacent}{-2}}{\stackrel{opposite}{1}}\impliedby \textit{let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{(-2)^2+1^2}\implies c=\sqrt{5} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=\cfrac{\stackrel{hypotenuse}{\sqrt{5}}}{\stackrel{opposite}{1}}\implies csc(\theta )=\sqrt{5}](/tpl/images/0330/7714/8dca3.png)
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Find the exact value of csc theta if cot theta = -2 and the terminal side of theta lies in quadrant...
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